Given the natural number $n$, which is in the form $p^2 \cdot q^2$ with $p$,$q$ prime numbers. Also $\varphi(n)$ is given. Describe a fast algorithm (polynomial time) that calculates $p$ and $q$. Apply your algorithm to calculate $p$ and $q$ when $n=34969$ and $\varphi(n)=29920$.
I found this problem on a mathematical competition on cryptography. I tried to find a solution alone and on the internet and I didn't succeed anywhere, can we find a solution?